A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations

2014 ◽  
Vol 351 (1) ◽  
pp. 340-357 ◽  
Author(s):  
Huamin Zhang ◽  
Feng Ding
Keyword(s):  
Iterative Algorithm ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Matrix Equations ◽  
Symmetric Positive Definite Matrix ◽  
Symmetric Positive Definite ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations

scholarly journals An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
Feng Yin ◽  
Guang-Xin Huang
Keyword(s):  
Iterative Algorithm ◽  
Special Kind ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Sylvester Matrix ◽  
Special Cases ◽  
The Matrix ◽  
Solution Pair ◽  
Sylvester Matrix Equations ◽  
Matrix Pair

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations(AXB-CYD,EXF-GYH)=(M,N), which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matricesXandY. When the matrix equations are consistent, for any initial generalized reflexive matrix pair[X1,Y1], the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation generalized reflexive solution pair[X̂,Ŷ]to a given matrix pair[X0,Y0]in Frobenius norm can be derived by finding the least-norm generalized reflexive solution pair[X̃*,Ỹ*]of a new corresponding generalized coupled Sylvester matrix equation pair(AX̃B-CỸD,EX̃F-GỸH)=(M̃,Ñ), whereM̃=M-AX0B+CY0D,Ñ=N-EX0F+GY0H. Several numerical examples are given to show the effectiveness of the presented iterative algorithm.

scholarly journals A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix

2017 ◽  
Vol 533 ◽  
pp. 95-117 ◽  
Author(s):  
Christos Boutsidis ◽  
Petros Drineas ◽  
Prabhanjan Kambadur ◽  
Eugenia-Maria Kontopoulou ◽  
Anastasios Zouzias
Keyword(s):  
Randomized Algorithm ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Symmetric Positive Definite Matrix ◽  
Symmetric Positive Definite
Sign in / Sign up

Export Citation Format

Share Document